3Q^2-16Q+57=45-Q

Solution for 3Q^2-16Q+57=45-Q equation:

Simplifying
3Q2 + -16Q + 57 = 45 + -1Q

Reorder the terms:
57 + -16Q + 3Q2 = 45 + -1Q

Solving
57 + -16Q + 3Q2 = 45 + -1Q

Solving for variable 'Q'.

Reorder the terms:
57 + -45 + -16Q + Q + 3Q2 = 45 + -1Q + -45 + Q

Combine like terms: 57 + -45 = 12
12 + -16Q + Q + 3Q2 = 45 + -1Q + -45 + Q

Combine like terms: -16Q + Q = -15Q
12 + -15Q + 3Q2 = 45 + -1Q + -45 + Q

Reorder the terms:
12 + -15Q + 3Q2 = 45 + -45 + -1Q + Q

Combine like terms: 45 + -45 = 0
12 + -15Q + 3Q2 = 0 + -1Q + Q
12 + -15Q + 3Q2 = -1Q + Q

Combine like terms: -1Q + Q = 0
12 + -15Q + 3Q2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -5Q + Q2) = 0

Factor a trinomial.
3((1 + -1Q)(4 + -1Q)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -1Q)' equal to zero and attempt to solve:

Simplifying
1 + -1Q = 0

Solving
1 + -1Q = 0

Move all terms containing Q to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1Q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1Q = 0 + -1
-1Q = 0 + -1

Combine like terms: 0 + -1 = -1
-1Q = -1

Divide each side by '-1'.
Q = 1

Simplifying
Q = 1
Subproblem 2
Set the factor '(4 + -1Q)' equal to zero and attempt to solve:

Simplifying
4 + -1Q = 0

Solving
4 + -1Q = 0

Move all terms containing Q to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1Q = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1Q = 0 + -4
-1Q = 0 + -4

Combine like terms: 0 + -4 = -4
-1Q = -4

Divide each side by '-1'.
Q = 4

Simplifying
Q = 4
Solution
Q = {1, 4}